Anomalous current from covariant Wigner functions

TL;DR

This paper derives a comprehensive formula for axial current in rotating fermionic media using covariant Wigner functions, revealing a topological component and connecting different baryon polarization approaches.

Contribution

It extends the calculation of axial current beyond small vorticity and chemical potential approximations, including a topological term and analyzing divergence.

Findings

Axial current includes a topological component along the 4-acceleration vector.

Higher order vorticity and chemical potential terms cancel in the massless limit.

Established similarity between different baryon polarization methods.

Abstract

We consider accelerated and rotating media of weakly interacting fermions in local thermodynamic equilibrium. Kinetic properties of this media are described by covariant Wigner function calculated on the basis of relativistic distribution function of particles with spin. We obtain the formulae for axial current beyond the approximation of smallness of thermal vorticity tensor and chemical potential and calculate its divergence. In the massless limit higher order terms in vorticity and chemical potential compensate each other with only the low-order contributions surviving. It is shown, that axial current gets a topological component along the 4-acceleration vector. The similarity between different approaches to baryon polarisation is established.